Citation: Kalay, O.C.; Karpat, E.; Dirik, A.E.; Karpat, F. A One-Dimensional Convolutional Neural Network-Based Method for Diagnosis of Tooth Root Cracks in Asymmetric Spur Gear Pairs. Machines 2023, 11, 413. https:// doi.org/10.3390/machines11040413 Academic Editor: Dan Zhang Received: 7 February 2023 Revised: 28 February 2023 Accepted: 21 March 2023 Published: 23 March 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). machines Article A One-Dimensional Convolutional Neural Network-Based Method for Diagnosis of Tooth Root Cracks in Asymmetric Spur Gear Pairs Onur Can Kalay 1 , Esin Karpat 2 , Ahmet Emir Dirik 3 and Fatih Karpat 1, * 1 Department of Mechanical Engineering, Bursa Uludag University, Bursa 16059, Turkey 2 Department of Electrical and Electronics Engineering, Bursa Uludag University, Bursa 16059, Turkey 3 Department of Computer Engineering, Bursa Uludag University, Bursa 16059, Turkey * Correspondence: karpat@uludag.edu.tr; Tel.: +90-224-2941930 Abstract: Gears are fundamental components used to transmit power and motion in modern industry. Their health condition monitoring is crucial to ensure reliable operations, prevent unscheduled shutdowns, and minimize human casualties. From this standpoint, the present study proposed a one-dimensional convolutional neural network (1-D CNN) model to diagnose tooth root cracks for standard and asymmetric involute spur gears. A 6-degrees-of-freedom dynamic model of a one- stage spur gear transmission was established to achieve this end and simulate vibration responses of healthy and cracked (25%–50%–75%–100%) standard (20 ◦ /20 ◦ ) and asymmetric (20 ◦ /25 ◦ and 20 ◦ /30 ◦ ) spur gear pairs. Three levels of signal-to-noise ratios were added to the vibration data to complicate the early fault diagnosis task. The primary consideration of the present study is to investigate the asymmetric gears’ dynamic characteristics and whether tooth asymmetry would yield an advantage in detecting tooth cracks easier to add to the improvements it affords in terms of impact resistance, bending strength, and fatigue life. The findings indicated that the developed 1-D CNN model’s classification accuracy could be improved by up to 12.8% by using an asymmetric (20 ◦ /30 ◦ ) tooth profile instead of a standard (20 ◦ /20 ◦ ) design. Keywords: deep learning; fault diagnosis; vibration signal; gear design; asymmetric gear 1. Introduction Gears are the key components of modern industry and have been widely employed in automotive, machinery, wind turbine, and aviation fields [1]. The operational reliability of a geared transmission system is mainly associated with its mechanical structure and life, which can be easily affected by internal and external factors [2]. Due to material defects and imperfect manufacturing procedures (e.g., machining error), insufficient lubrication, and harsh running environments, the gears are prone to local defects [3,4]. According to the statistics, around 60% of total gearbox faults originate from individual gear errors [5]. In addition to that, it has also been reported that approximately 19.1% of helicopter powertrain system failures are caused by gearbox systems [6]. Typically, the main gear failure modes include tooth root cracks, pitting, spalling, and tooth surface wear. With this in mind, the literature review confirms that the early diagnosis of tooth root cracks is considerably valuable in modern industry in terms of predictive maintenance since the tooth cracks tend to have a more rapid failure (e.g., complete tooth breakage) compared to other listed major failure modes [7,8]. The presence of a tooth root crack can deteriorate the dynamic responses, for example, vibration and transmission error (TE), of a gear pair and may threaten the machines’ safety. To avoid unscheduled shutdowns, massive economic (for example, maintenance and repair costs) losses, and even human casualties, the matter of gear condition monitoring (CM) has drawn attention during the last decade with the wide availability of sensors and ever-increasing computation power. From this standpoint, Machines 2023, 11, 413. https://doi.org/10.3390/machines11040413 https://www.mdpi.com/journal/machines